"If you're running the operation, you really can't step out of line," said Richard Haver, who spent 34 years in the federal government specializing in intelligence operations. Petraeus himself would have had to severely discipline if not fire any agency employees involved in similar behavior, said Haver, who is retired after having served as deputy for community affairs for the intelligence community.

"You're compromising, potentially, your security."

Haver called Petraeus' resignation "the honorable thing to do," but added, "I don't understand, knowing that man, how this could have happened. ... I think it's a real tragedy. I thought he was a great guy, but I think he did the right thing, under the circumstances."

The retired four-star general who commanded forces in Iraq and Afghanistan said he is devastated that he has hurt his wife of more than 37 years and that she is "far better than he deserves," a source told HLN's Kyra Phillips. "I spent a lot of time with him on the battlefield," she said. "This is the last person I ever expected to do something like this."

JUST WATCHED

C.I.A. Director resigns over affair

MUST WATCH

A U.S. official told CNN that the FBI initiated an investigation after receiving a tip that Petraeus was involved with Paula Broadwell, a co-author of his biography.

The concern was that he could potentially be blackmailed or put "in a vulnerable spot," the official said.

Broadwell had spent a year with Petraeus in Afghanistan for the book, "All In: The Education of General David Petraeus."

"She had incredible access" and others noticed, said Fran Townsend, CNN national security contributor and a member of the CIA's External Advisory Committee. "There's bound to be some sniping and gossiping, but I don't think anybody took it seriously," she said. "He seemed beyond reproach; he worked incredibly hard; he was incredibly competent."

It was not clear whether Broadwell was the woman with whom Petraeus had an affair. CNN has not been able to reach her for comment.

The White House would likely have known about the FBI investigation into the tip before it received Petraeus' letter, Townsend said.

Whenever the FBI opens a criminal investigation of a senior Cabinet official or administration official, "they've got to make notifications of that," she said.

Director of National Intelligence James Clapper would probably have notified the White House chief of staff or the national security adviser, she said.

CNN Contributor and former CIA officer Robert Baer said the public announcement of the affair was uncharacteristic and implies more may have happened than has been revealed.

"Something like this doesn't come out and blow his career up unless something else is going on," Baer said. "Normally, when a CIA director resigns under this sort of pressure, he'd do it quietly. He'd say he was doing it for family reasons. He'd go off, we'd never hear any more about it. Somebody would write a book 10 years later, but to use it in his resignation letter is extraordinary."

But CNN's Pentagon correspondent, Barbara Starr, said the simplest explanation may be the most likely one. "David Petraeus, for decades, likes to control the circumstances around him," she said. "Clearly, this was a character lapse in which he slipped out of control of his circumstances. This (going public) is a way he could bring it back. He could limit the damage, not have the Washignton drip drip of stories every day, try and do everything he could to not humiliate his wife any further, cause any further embarrassment to his grown children, one who is an Afghanistan veteran. This, I think, is classic Petraeus trying to control what is going on around him."

If so, the letter would dovetail with number five on a list of Petraeus' 12 rules for living, which Broadwell published on November 5 on the Daily Beast: "We all will make mistakes. The key is to recognize and admit them, to learn from them, and to take off the rear-view mirrors -- drive on and avoid making them again."

Petraeus had little choice but to resign, said Austin Long, assistant professor at Columbia University's School of International and Public Affairs.

"It is a counterintelligence issue," he said, referring to the potential that a man with security clearance could wind up being coerced. "It's not that nobody at the agency has affairs, but if you get caught on them, that's an avenue to be coerced."

In addition, "the Army takes a very dim view of extramarital affairs -- if you are busted," said Long, whose research interests include intelligence.

It is the rare marriage, he said, that can withstand many months apart from one's spouse, as occurred often during Petraeus' career of multiple deployments.

Finally, Petraeus may simply be trying to limit any damage to a possible political career.